Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose significant challenges. In case of Causal Bayesian Networks (CBNs), Pearl assumes autonomy of mechanisms that determine interventions to calculate a range of probabilities. We show that by making simple yet often realistic independence assumptions, it is possible to uniquely estimate the probability of an interventional formula (including the well-studied notions of probability of sufficiency and necessity). We discuss when these assumptions are appropriate. Importantly, in many cases of interest, when the assumptions are appropriate, these probability estimates can be evaluated using observational data, which carries immense significance in scenarios where conducting experiments is impractical or unfeasible.

翻译：因果模型对于理解复杂系统和识别变量间的因果关系至关重要。尽管因果模型已得到广泛应用，但涉及干预的公式条件概率计算仍面临重大挑战。针对因果贝叶斯网络（CBNs），Pearl 假设决定干预的机制具有自主性，从而计算一系列概率。我们证明，通过建立简单且通常符合实际的独立性假设，可以唯一地估计干预公式的概率（包括已被深入研究的充分性概率和必要性概率）。我们讨论了这些假设的适用条件。重要的是，在许多关注场景中，当假设成立时，这些概率估计可以利用观测数据进行评估，这在开展实验不切实际或不可行的情况下具有重大意义。